Vibrating rotor gyroscope



May 14, 1968 H. F. ERDLEY VIBRATING ROTOR GYROSCOPE 5 Sheets-Sheet 1Filed May 21, 1965 Rwy Y E JVQ WED/0 15 FIG w W #WL SUPPLY United StatesPatent 3,382,726 VIBRATING ROTGR GYROSCOPE Harold F. Erdley, PacificPalisades, Calif, assignor to Litton Systems, Inc, Beverly Hills, Calif.Filed May 21, 1965, Ser. No. 457,740 21 Claims. (Cl. 74--5.6)

The present invention relates in general to navigational and positionalinstruments and in particular to improved vibrating rotor gyroscopes.

One form of vibrating rotor gyroscope, an inertial instrument possessingmany advantages over conventional gyroscopes, is described in copendingapplication entitled Vibra-Rotor Gyroscope by H. F. Erdley et 211.,Serial No. 323,985, filed Nov. 15, 1963, and assigned to the sameassignee as the present application. In general, a vibrating rotorgyroscope comprises an inertial element which is co axially mounted on arotating shaft. The inertial element rotates with the shaft and hastorsionally restrained vibrational freedom about its mounting axis whichis angularly disposed (ordinarily perpendicular) to the shaft. Thevibrating rotor gyroscope is designed so that the natural frequency ofvibration of the inertial element about the mounting axis is equal tothe frequency of shaft rotation (N) in order to make the inertialelement very sensitive to motions at right angles to the axis of theshaft. An external angular displacement (rotation) of the vibratingrotor gyroscope around any axis, except the spin axis, causes theinertial element to vibrate at its natural frequency, the maximumamplitude of such vibration being proportional to the angulardisplacement. In addition, the phase of the vibration relative to atiming signal is a direct measure of the direction of the angulardisplacement. Hence, the vibrating rotor gyroscope may be used in placeof a direct reading, two-degree-of-freedom gyroscope.

Since the vibrating rotor gyroscope requires no complicated gimbalsuspension system or flotation fluid, it has an extremely low drift rateand is far superior to conventional gyrosc-opes. Due to the fact,however, that the sensitivity of the inertial element to external forcesis dependent upon the natural frequency of vibration of the inertialelement being equal to th frequency of shaft rotation, any spuriousforces or vibrations which act in the equations of motion of thevibrating rotor gyroscope as driving forces of a frequency equal to thefrequency of shaft rotation cause, as more fully explained hereafter, anoutput error signal to appear which is indistinguishable from the outputcaused by an external angular displacement. It has been found that suchspurious output signals can be generated in the prior art devices by aninherent shaft wobble of frequency 2 N due to the tolerances in thebearing mechanism supporting the rotating shaft of the vibrating rotorgyroscope and, under certain circumstances, can cause undesirable errorsto appear in the output signals obtained from operational angulardisplacements of the vibrating rotor gyroscope.

The present invention has succeeded in overcoming all of theabove-mentioned disadvantages of the prior art devices by providing avibrating rotor gyroscope in which a plurality of inertial elements arecoaxially mounted on a single shaft in such a manner that the outputsignals therefrom maybe combined to eliminate the component of theoutput signals due to vibrational forces. In addition, since there arenow a plurality of inertial elements on a single shaft, both rotationaland accelerational information can be obtained from the same instrument.

It is therefore the primary object of the present invention to provide anew and improved vibrating rotor gyroscope.

It is another object of the present invention to provide a vibratingrotor gyroscope capable of cancelling spurious outputs caused by 2 Nfrequency vibrations.

'ice

It is a further object of the present invention to provide a vibratingrotor gyroscope capable of providing both rotational and accelerationalinformation.

It is still another object of the present invention to provide avibrating rotor gyroscope having a plurality of independently mountedinertial elements.

-It is a further object of the present invention to provide a vibratingrotor gyroscope having a plurality of coaxially mounted inertialelements whose suspension means are angularly disposed from one another.

It is another object of the present invention to provide a vibratingrotor gyroscope having a plurality of inertial elements, at least one ofwhich has its center of mass displaced a preselected distance from itspoint of suspension.

The novel features which are believed to be characteristic of theinvention, both as to its organization and method of operation, togetherwith further objects and advantages thereof, will be better understoodfrom the following description considered in connection with theaccompanying drawings. It is to be expressly understood, however, thatthe drawings are for purposes of illustration and description only andare not intended as a definition of the limits of the invention.

FIGURE 1 is a cross-section view of a preferred embodiment of thepresent invention;

FIGURE 2 is a simplified, perspective drawing of the embodiment ofFIGURE 1 illustrating the principles of operation of the presentinvention;

FIGURE 3 is a block schematic diagram of a vibrating rotor gyroscopesystem for cancelling spurious output caused by 2 N frequency forces;

FIGURE 4 is a block schematic diagram of a vibrating rotor gyroscopesystem for obtaining rotational and accelerational information;

FIGURES 5 and 6 illustrate further modifications of the presentinvention; and

FIGURE 7 illustrates a vibrating rotor gyroscope arrangement forobtaining complete accelerational and rotational information free fromspurious outputs caused by 2 N frequency forces.

In reference now to FIGURE 1, the vibrating rotor gyroscope 10 of thepresent invention is shown comprising a cylindrical outer casing 11 anda support member 12 attached thereto upon which is positioned the stator14 of a constant speed synchronous hysteresis motor 16. The rotorelement 18 of the synchronous motor 16 is affixed to a spin shaft 20which is driven to rotate on ball bearings 22 about the stator 14. Theouter case 11 is preferably pressure tight and in the preferredembodiment thereof is completely evacuated or alternatively contains acontrolled low density atmosphere as of hydrogen or helium, and isgenerally constructed of a light, but rigid, material such as aluminum.The spin shaft 20 is constructed of a rigid material such as stainlesssteel. Inertial elements 26, 26 (shown here in the form of rings) of thevibrating rotor gyroscope are mounted on the spin shaft 20 by means oftwo orthogonal pairs of cruciform-shaped torsion bars 28, 28, a pair ofcentral supports 30, 3t) and mounting screws 29, 29'. It should be notedthat since the torsion bars 28 are orthogonal to the torsion bars 28,the torsion bars 28 are not visible in this cross-sectional view.Although the inertial elements 26, 26' may be constructed completely ofa rigid, lowreluctance material such as iron or steel, in the embodimentshown it has been chosen to surround a light-weight rigid material (suchas titanium) with iron or steel rings 32, 32 in order to reduce theweight of the inertial elements 26, 26'.

In the present embodiment, the center of mass (C.M.) of each of theinertial elements 26, 26 is located at the point of suspension of eachof the inertial elements 26, 26', i.e. where the axis of rotation[defined by the axis of the spin shaft 20] intersects the axis ofvibration (defined by the axis of the torsion bars 28, 28). Under theseconditions the gyroscope 10 is substantially insensitive toac-celerational forces. As explained hereafter, however, the gyroscope10 may be made sensitive to aecelerational forces (and capable of thedetection thereof) by placing the center of mass a preselected distancefrom the point of suspension, preferably along the spin shaft 20. Thismay be accomplished, for example, by making the inertial element 26heavier on one side by the addition of weights thereto or the milling ofmaterial from the other side thereof. In addition, as shown hereafter,more than two inertial elements may be placed on the spin shaft 20 inorder to obtain complete information on the accelerational androtational forces acting on the gyroscope.

In operation, the synchronous motor 16 (driven by power supply 38)causes the inertial elements 26, 26' to rotate at a predeterminedfrequency N. In order to better appreciate the operation of the presentinvention and to understand the importance of cancelling out spurious 2Nfrequency forces, reference may be had to FIGURE 2 and to the followingmathematical analysis of the properties of the invention.

The approximating basic differential equation of motion of one of theinertial elements of the invention may be found from Eulers equationsfor the motion of a rigid body about a fixed point. The ordinary torqueequation, L:J, where J (angular momentum) and L (torque) are bothdefined in a system of axes which has a fixed orientation in space,becomes when transformed into a system of axes fixed in a rotating body:

for the component of torque around the rotating y axis, I and w beingthe moments of inertia and the angular velocities around theirrespective rotating axes. If it is assumed that the rigid body is a ringrotating around the z axis, then I =I =A and I =C, where A is thetransverse and C is the polar moment of inertia. If the above equationis then equated to the torques around the y axis due to restraining(spring) and damping forces, the basic equation for the system becomes:

Aw -l- (A-C)w w +D9-]-K0=O (2) where K is the angular spring constantand D is the angular damping constant of the torsion bars 28, and is theangular excursion of the inertial element 26 measured as a rotationaround the y axis.

If the shaft 20, spinning at a frequency N, experiences an angulardisplacement around an axis orthogonal to the shaft 20 then:

where sin 9:0, cos 0:1, @5 0. Inserting Equations 6, 7, and 8 intoEquation 2, the basic equation of motion becomes:

A D+ K+N c A 0=cN sin Nz Al;3 cos Nr which can be recognized as theequation of a damped forced harmonic oscillator. Since it is desirablethat the system have its natural frequency of oscillation at the drivingfrequency N, the spring constant K must be chosen so that:

AN =K+N (CA) 10 K=N2(2AC) and the basic equation of motion becomes:

A'+D0'+AN 0=cN sin Nr-A i' cos Nt 12) If it is assumed that the rate ofchange of the angular displacement is a constant (which inherently makes:0), the damping constant D is small, and the time constant of thesystem T, defined as 2A/D, is very much greater than t, the solution toEquation 12 can be approximated by:

to z =2-- T 6(1) D T cos At (13) This equation demonstrates that forsmall angles the angular excursion of the inertial element 26 isdirectly proportional to the rotational displacement git of the shaft20, multiplied by a cosine term representing the vibrations. Although itis not expressly stated in the above equation, the cosine term containsphase information which can be extracted by means of a timing signal toyield the angle between the direction of the rotational displacement ofthe shaft 20 and a coordinate system fixed in the outer case 11 of thegyroscope.

If the shaft 29 of the gyroscope is subjected to vibrations of a 2 Nfrequency, the vibrations are rectified by the system and appear in theangular excursion 0 of the inertial element 26 as a spurious rotationaldisplacement. This fact can be made more apparent by the follow ingmathematical analysis. The vibrations can be represented by:

Substituting Equations 14, 15, and 16 into Equation 12 and noting theidentities:

sin 2Nt sin Nt= /z (cos Nt-cos 3N1) cos 2Nt sin Nt= /z (sin Nzsin 3Nr)cos 2Nt cos Nt= /2 (cos Nt+cos 3Nt) sin 2Nt cos NZ= /2 (sin N1. sin 3Nt)and the fact that the system is very insensitive to vibrations offrequency 3N, the following equation of motion is obtained:

A +D0 +AN 0 =N (2A-C) (G cos Nz+H sin N!) (18) Using the previousassumptions, the solution to Equation 18 can be approximated by:

cos Nt+tarr It is apparent the Equation 19 is identical in form toEquation 13 and thus an output signal is generated by the spurious 2 Nfrequency forces Which cannot be separated by prior art devices from theouput generated by true rotational displacement.

In the preferred embodiment of the present invention, however, thespurious output signal is cancelled by using two inertial elements 26,26' mounted on the shaft 20 with their torsion bars 28, 28' atsubstantially right angles to one another. In this case, the basicequation of motion for the second inertial element is given by:

into which Equations 14, 15, and 16 can be inserted, as before, toyield:

A0 -{-D!) +AN 0 :N (2AC) (G sin Nt-H cos N!) K o +H t Q cos (Ni tan 1 H(22) If Equations 19 and 22 are then summed:

but since then:

and thus the spurious output signal does not appear in the summed outputsignals generated (as hereafter shown) by the inertial elements 26, 26'.

In FIGURE 1, E-shaped sensor arrangements 40, 40', each composed of aC-shaped ferrite material with a permanent magnet central leg, arepositioned adjacent to inertial elements 26, 26 (and iron rings 32, 32')and are attached to the outer case 11 of the vibrating rotor gyroscopeby support members 32, 42. The permanent magnet central legs of theE-shaped sensor arrangements 40, 49 cause D.C. magnetic fields to existin the closed fiux paths defined by the central and outer legs of thesensor arrangements 40, 40 and the iron rings 32, 32. Any vibratorymotions of the iron rings 32, 32' cause a change in the reluctance ofthe portions of the paths between the central and outer legs of thesensor arrangements 40, 40. Consequently, the vibrations of the ironrings 32, 32 cause A.C. magnetic fields to be generated in the windings(and output leads) 47, 47, which fields in turn generate A.C. signals(the outputs of the sensor arrangement 40, 40) representative of thevibratory motion of the inertial elements 26, 26. While the sensingsignals have been obtained by using D.C. magnets for the central legs ofthe sensor arrangements 40, 46, many other techniques are possible. Forexample, A.C. magnetic fields can be generated (in the closed fluxpaths) by coupling A.C. generators to ferrite central legs of the sensorarrangements 49, 40'. Since the edges of the iron rings 32, 32 nearestthe sensor arrangements 49, 40' are not only vibrating but alsorotating, the frequency of the electromotive forces generated by thepositional or velocity changes of the iron rings 32, 32' is a functionof both such motions and is primarily equal to the sum of the frequencyof rotation and the frequency of vibration (a small difference frequencyterm also being present). Thus, in the sensor arrangement of the presentembodiment, the sensing signal has (in the ideal case) a frequency of 2N.

In order to resolve the output signals from the sensor arrangements 40,40 into components along the set orthogonal axes fixed in the outer case11 (to determine the direction of the angular displacement of the shaft20 relative to such axes), a timing signal having a frequency 2 N isgenerated. A C-shaped timing generator 51 is shown aflixed to the outercase 11 by supporting member 12 and comprises a C-shaped permanentlymagnetized ferrite structure with a sensing coil (and output lead) -11Wound thereon. A rotating ferrite member 36 (which forms part of theclosed flux path) is constructed with a very slight ellipsoidalconformation so as to vary the reluctance of the magnetic path betweenthe legs of the C-shaped timing generator 51. Since the C-shape-d timinggenerator 51 is stationary, the position of the rotating member 36 overthe two ferrite legs oscillates radially during each revolution of theshaft 20. For each revolution of the shaft 20, the radial oscillation ofthe member 36 causes it to assume maximum and minimum spacings from thetiming generator 51 twice during each revolution. Thus, during eachrevolution of the shaft 20 alternate minimum reluctance and maximumreluctance paths are twice formed between the two legs of the C-shapedtiming generator 51. Since the reluctance of the magnetic path variesthrough two maximums and two minimums each revolution, an A.C.electromotive force is generated in sensing coil (and output lead) 51'having a frequency twice that of the frequency of revolution of theshaft 20. This A.C. electromotive force is used to provide a timingsignal of frequency of 2 N. By circumferentially varying the position ofthe timing generator 51 around the shaft 20, the two maximum amplitudepoints (or minimum amplitude points) of the timing signal can be made tooccur when the torsion bars 28, 28 are parallel and orthogonal,respectively, to one of the case-referenced orthogonal axes. If suchcoincidence does not occur, the timing signal will be resolved intocomponents along orthogonal axes rotated a determinable angle from thecase-referenced axes. These two set of axes can be brought intocoincidence, however, by shifting the phase of the timing signal.

As illustrated in FIGURE 3 wherein the gyroscope 10 is depicted insymbolic form, the timing signal from the timing generator is fed vialead 51' into a standard phase shifter 54 which provides two timingsignals, one shifted in phase from the other by In an alternativeembodiment, a second timing generator may be employed displaced 45circumferentially from timing generator 51 to provide the second timingsignal shifted in phase by 90. The timing signals are coupled along withthe sensing signals from the sensor arrangements 40, 40' (via leads 47,47') to standard demodulators 50, 50 (of the type, for example,described in the above-cited patent application). The demodulato-rs 50,50- provide signals 0(X) :2N(X), 0(Y):2N(Y) which represent themagnitudes of the components of the rotational displacement plus orminus the components of the 2N frequency movements of the shaft 20 alongthe X and Y coordinates of the case-referenced axes. Since demodulators50, 50' receive each two timing signals and provide each two outputsignals, demodulators 50, 50' may each consist of two separatedemodulators or a single composite demodulator with two input and outputchannels. In addition, demodulators 50, 50' may also include R-Cnetworks to filter the signals generated thereby.

As stated previously (and as shown above), each of the output signalsfrom the vibnating rotor gyroscope is composed of signals generated bytrue rotational displacement forces and spurious 2N frequency forces.Since, however, the output signals caused by such spurious forces aregenerated by two inertial elements having their axes of vibration (i.e.suspension means) orthogonal and thus are opposite in polarity, theoutput from demodulator 50' contains spurious signals of one polaritywhile the output from demodulator 50 contains the same spurious signalsbut of opposite polarity. The output signals from demodulators 50 and 50are thus coupled to standard summing circuits 70, 70, composed ofaddition circuit 97 and sign inverter 99, which add the Y and Xcomponents, respectively, of the sensor outputs and, in so doing,provide signals 0(X), 9(Y) representative of the magnitudes of therotational displacement free from the spurious signals 2N (X), 2N(Y)generated by the 2N frequency forces.

It should be noted that, as previously stated with respect to the anglebetween the shaft and mounting axis, the suspension means do not have tobe orthogonal but may be angulariy disposed. In such a case, however,the 2N frequency tennis are not completely eliminated but partiallyremain with their magnitude being proportional to the cosine of theangle between the suspension means.

Since the validity of Equation 13 describing the angular excursion 0 ofthe inertial elements 25, 26 is predicated upon the time of applicationof a particular shaft displacement rate being very much less than thetime constant of the system, it is desirable that torquing forces beapplied to the vibrating rotor gyroscope to null such vibratory motion.In an inertial guidance system, the vibratory motion is usually nulledby rotating the platform upon which the vibrating rotor gyroscope ismounted (and hence applying a mechanical torquing force to displace theshaft The X and Y outputs are thus shown as coupled to networks 74, 76(which may, for example, be standard switching circuits or s-witchincircuits coupled with mixing circuits) adapted to apply via terminals71, 71' such signals to the rotators of the inertia guidance platform,as illustrated in the above-cited patent application. In many otherinstances, however, it is desirable to be able to null the vibratorymotion of the inertial elements 26, 26 without displacing the shaft 20.This occurs, for example, when the vibratory rotor gyroscope is fixedelymounted in an aircnaft or on the earth and the vibratory motion inducedby the aircraft motion or the earth rate must be nulled in order to usethe sensing signal generated thereby for reference purposes. On theother hand, it is desirable to be able to directly induce vibratorymotion of the inertial elements 26, 26 to correct for positional orguidance errors and use the sensing signal generated thereby to effectmechanical torquing of the shaft 20 (to null the induced vibratorymotion). For this purpose, feedback leads 7?, 80 are shown leading fromnetworks 7 76 to the vibrating rotor gyroscope itself to apply X axisand Y axis torquing forces, respectively, as explained hereafter, to theinertial elements 26, 26. In addition, inputs 82, 84 are coupled to thenetworks 74, 76 to allow external biasing signals to be introduced (viasuch switching circuits) when desired into the system.

In the present invention, the vibratory motion of the inertial elements26, 26 can be nulled (or induced) by applying torquing forces directlyto the inertial elements 26, 26 (and the iron rings 32, 32) of thevibrating rotor gyroscope. As shown in FIGURE 1, two E-shaped torquerarrangements 62, 62 are mounted to the outer case 11 of the vibratingrotor gyroscope by support arrangements 66, 66' along, for example, theX axis of the case-referenced coordinate system. Mounted 90 therefrom,but not illustrated, are two more torquer arrangements which act alongthe Y axis of the case-referenced coordinate system. The E-shapedtorquer arrangements 62, 62' are composed of C-shaped ferrite pieceswith permanent magnet central legs. The network 74 provides torquingsignals via leads 78, 78 to the outer legs of the torquer arrangements62, 62 acting along the X axis; similarly, the network '76 providestorquing signals via leads 80, G9 to the outer legs of the torquerarrangements acting along the Y axis. Depending upon the polarity of thetorquing signals applied by the network 74, the magnetic field betweenthe central leg and one of the two outer legs of each of the E-shaped Xaxis torquer arrangements 62, 52 is increased, while the magnetic fieldbetween the central leg and the other outer leg is decreased. Network 76effects a like result in the Y 'axis torquing arrangements. Thus, theselective application of torquing signals by the networks 74, 76 to theX axis and Y axis torquer arrangements generate magnetic torquing fieldswhich can oppose, reinforce, or induce vibnatory motion of the inertialelements 25, 26 in the same manner as if an angular displacement wereapplied to the shaft 20.

A modification of the vibrating rotor gyroscope of the present inventionis illustrated (symbolically) in FIGURE 4. In FIGURE 4, two inertialelements 26, 26 are shown with their suspension means 28, 28' parallelto one another. One of the inertial elements (26) has its center of mass(C.M.) displaced (as described previously), a preselected distance alongthe shaft 2% from the point of suspension of the inertial element. Sincethe center of mass is displaced from the point of suspension, anacceleration along any direction, except that of the shaft, produces amoment on the inertial element. This moment. it can be shown, appears inequations of motion of the vibrating rotor gyroscope exactly like anangular displacement it; since, however, the moment produced by anacceleration is orthogonal to the acceleration causing it, an angulardisplacement about and an acceleration along a particular axis appear 90out of phase in the equations of motion. In a typical case, for apendulosity of .4 grn.-crn. (the product of the pendulous mass and thelength of the pendulum arm) and an inertial element weighing 40 gms.,the center of mass would be displaced approximately .01 cm. from thepoint of suspension.

Thus, the output signal from the sensor of a vibrating rotor gyroscopewith its center of mass displaced contains components not only ofrotational displacement but also of acceleration. In order to separateout the component of acceleration without the use of a separateaccelerometer, a second inertial element is used which is substantiallyidentical to the first but with its center of mass at its point ofsuspension. As shown in FIGURE 4, output signals H(X)+2N(X), 6(Y) +2N(Y)are derived by phase shifter 54 and demodulator 50 from inertial element26 having its center of mass at its point of suspension while outputsignals 6(X) +A (X) +2N(X), 0(Y) +A(I) +2N(Y) representative of themagnitude of the components of the rotational displacement plus theacceleration plus the 2N frequency movements of the shaft 213 arederived by phase shifter 54 and demodulator 50 from inertial element 26having its center of mass displaced a preselected distance from itspoint of suspension. The output signals from the inertial element 26 arethen subtracted from those of inertial element 26' by standarddifferencing networks, 0, 9i) to yield the signals A(X), A(Y)representative of the components of the acceleration. Terminals 73, 73are provided to couple the signals A(X), A(Y) to an external recordingmeans, such as a computer.

It should be noted, however, that in accordance wtih the solutions ofthe vibrating rotor gyroscope, the accelerational information is reallythe acceleration times the time it has been applied, or the velocity. Inorder to obtain true acceleration information, the output signals A(X),A(Y) are fed back via leads 78, to the torquing elements of thevibrating rotor gyroscope to operate it in a closed loop operation.Since the angular excursion of the inertial element is constantly beingtorqued back to null, the informational output is therefore a trueacceleration. In addition, the signals 0(X), 6(Y) may be fed back to thetorquers by coupling the signals from terminals 71, '71 to terminals 91,93.

It should be noted in FIGURE 4 that the outputs of both of the inertialelements 26, 26" contain 2N frequency terms of the same polarity sincethe suspension means 28, 28 are parallel. Because of this, therotational displacement terms 6(X)+2N(X), 0(Y)+2N(Y) retain 2N frequencyterms in their final form while the accelerational terms A(X), A(Y) uponsubtraction of the two outputs, emerge free from any 2N frequency terms.If, moreover, the suspension means 28, 28' were orthogonal, it is easilyseen that the rotational displacement terms would retain the 2Nfrequency term while the accelerational terms would have 2N frequencyterms added to it. If it is considered more desirable to eliminate the2N frequency terms from the rotational displacement terms and to allowthem to remain in the accelerational terms, the embodiment of thegyroscope 10 and the circuitry therefor shown in FIGURE 5 can be used.In this embodiment, the suspension means 23, 28' for the inertialelements 26, 26 are orthogonal, while the centers of mass of theinertial elements 26, 26 are displaced in opposite directions from theirrespective axes of vibration, i.e. towards one another or away from oneanother rather than in the same direction (as in FIGURE 7). The outputsignals obtained from each of the sensors 43, 4d of the inertialelements 26, 26' are demodulated and mixed in a manner similar to thatin FIGURES 3 and 4 to yield the output signals K )l It can easily berecognized that with only four outputs available from a two inertialelement vibrating rotor gyroscope (X and Y terms from each inertialelement), the six variables in the output signals, i.e., (X), 0(Y),A(X), A(Y), 2N(X), and 2N(Y) cannot be individually determined. Thislimitation, however, is overcome by the embodiment of the gyroscope 10(and the circuitry therefor) shown in FIGURE 6 in which three inertialelements 26, 26, 26" are coaxially mounted on a single shaft 20. One ofthe elements (26) has its center of mass displaced a preselecteddistance from its point of suspension, while the other two inertialelements (26, 26") have their suspension means 28', 28" orthogonallydisposed. Since there are now 6 outputs (X and Y terms from eachinertial element), the six variables recited above can be individuallydetermined. The output signals of each of the three inertial elementsare demodulated and mixed in a manner similar to the previousembodiments to yield the signals 0(X), 0(Y), A(X), A(Y), 2N(X), 2N(Y) onterminals 71, 71', 73, 73' and 75, 75. It should be noted that thesignals 2N(X), 2N(Y) are coupled back to the torquers via leads 78, 80to prevent undue oscillations being built up by the 2N vibrationalforces.

It is apparent that the embodiments illustrated in FIGURES 3 through 6can be used as the sensing elements on an inertial platform. Since,however, a single vibrating rotor gyroscope can only measureacceleration and rotational displacement -(or rate) along two axes, twoor more of such gyroscopes must be combined to give completethree-dimensional information. As stated above, moreover, unless thereare sufficient outputs from the inertial elements of the gyroscope allof the rotational, accelerational, and 2N frequency terms cannot beindividually determined. If, for example, two of the vibrating rotorgyroscopes illustrated in FIGURE 3 are placed orthogonal to one another,the eight outputs therefrom (X and Y terms from each inertial element)yield a sulficient amount of information to individually determine theseven variables, i.e. the three rotational terms and the four 2Nfrequency terms (two from each gyroscope). If the gyroscopes in FIGURES4 and 5 are utilized, however, it can be easily recognized that theeight outputs therefrom will be unable to yield sufficien-t informationto separate the ten variables, i.e. three rotational terms, the threeaccelerational terms, and the four 2N frequency terms. If, however, twoof the vibrating rotor gyroscopes illustrated in FIGURE 6 are placedorthogonal to one another, the twelve outputs obtainable therefrom aremore than suflicient to resolve the three accelerati nal, threerotational, and four 2N frequency terms.

In certain instances, however, it may not be desirable to place threeinertial elements on a single shaft; In FIGURE 7 an embodiment of thevibrating rotor gyroscope utilizing only two inertial elements on asingle shaft to determine rotational, acce'lerational and 2N frequencyterms is illustrated. In this embodiment, three vibrating rotorgyroscopes 19a, 12, 0 (each with two inertial elements) are mounted onan inertial element 13 orthogonal to one another. Since a singlevibrating rotor gyroscope (such as shown in FIGURE 4) can determineacceleration only along two coordinate axes, at least two of thegyroscopes r1042, 11, 0 must have the center of mass of an inertialelement spaced a preselected distance from the point of suspension todetermine A(X), A(Y), A(Z). Since there are now three sucn gyroscope-s,it can be recognized that there are twelve variables, i.e. threerotational terms, three accelerational terms, and six 2N frequency terms(two for each gyroscope). Thus, the twelve outputs of the threegyroscopes yield just enough information to separate all the variables.However, the centers of mass of the inertial elements of the variousgyroscopes must be properly placed so as to avoid duplication of outputsignals. If the inertial elements of one of the three gyroscopesgenerate the same information as the inertial elements of another one ofthe three gyroscopes, then all of the variables cannot be individuallydetermined. In the particular embodiment shown, the gyr0scope (10a)supplying the X and Z coordinate rotational and accelerational terms hasthe centers of mass of the inertial elements displaced from the pointsof sus ension a preselected distance away from the origin O of thestationary reference coordinate system located in the inertial elernent13. On the other hand, the gyroscope (10c) supplying the Y and Zcoordinate rotational and accelerationa'l terms has the centers of massof the inertial elements displaced from the point of suspension apreselected distance towards the center of such coordinate system. Ifthe centers of mass of the inertial elements of the gyroscopes 10a andwere not displaced in an opposite manner with respect to the origin ofthe reference coordinate system, the A(Z) terms would be of the samepolarity and the 0(Z)+A (Z) ter'm could not be separated. As is seenfrom the circuitry illustrated in FIGURE 7, the rota tional andaccelerational output signals generated by each of the gyroscopes 1012:,b, 0 can be demodulated and mixed to yield all six rotational andaccelerational variables; since each of the gyroscopes has itssuspension means orthogonal, it is apparent that all six of the 2Nfrequency terms can be eleminated (and solved for if desired). Theoutput signals, available on terminals 71, 71', 711" 73, 73', 73", canbe fed back to X, Y, Z torquer terminals 91, 93, 95, respectively,coupled to the rotators of an inertial platform such as shown in theaforementioned patent application, or stored in a computer forprocessing.

Having thus described the invention, it is obvious that numerousmodifications and departures may be made by those skilled in the art;thus, the invention is to be construed as being limited only by thespirit and scope of the appended claims.

What is claimed is: I

1. An inertial instrument comprising: a frame; a plurality of inertialelements rotatable with respect to said frame about a first axis, saidinertial elements being capable of rotationally restrained vibratorymotion about axes of vibration rotating with said inertial elements andangularly disposed 'with respect to said first axis; and means forrotating said inertial elements about said first axis.

2. The inertial instrument of claim 1 further comprising sensor meansresponsive to the vibratory motion of said inertial elements forgenerating signals representative of said vibratory motion.

'3. The inertial instrument of claim 2 further comprising means coupledto said sensor means and responsive to signals therefrom for generatingoutput signals representative of rotational movements of said inertialinstrument.

4. The inertial instrument of claim 3 further comprising means forreducing the magnitude of the components of said output signals causedby vibrational forces acting on said inertial elements.

5. The inertial instrument of claim 3 wherein said means coupled to saidsensor means further comprises means for generating signalsrepresentative of vibrational forces acting on said inertial elements.

6. The inertial instrument of claim 5 further comprising means operableon said inertial elements and responsive to said output signalsrepresentative of said vibrational forces for substantially continuouslynulling the vibratory motion of said inertial elements caused by saidvibrational forces.

7. The inertial instrument of claim 1 wherein at least one of saidinertial elements has its center of mass displaced a preselecteddistance from its axis of vibration.

8. The inertial instrument of claim 7 further comprising meansresponsive to the vibratory motion of said inertial elements forgenerating output signals representative of accelerational movements ofsaid inertial instrument.

9. The inertial instrument of claim 8 further comprising means operableon said inertial elements and responsive to said signals representativeof said accelerational movements for substantially continuously nullingthe vibratory motion of said inertial elements caused by saidaccelerational movements.

10. The inertial instrument of claim 1 further comprising means forapplying torquing forces to said inertial elements to control thevibratory motion thereof.

11. An inertial instrument comprising: a frame; a plurality of inertialelements rotatable with respect to said frame about a first axis, saidinertial elements being capable of rotationally restrained vibratorymotion about axes of vi ration rotating with said inertial elements andsubstantially orthogonal to said first axis; and means for rotating saidinertial elements about said first axis.

12. The inertial instrument of claim 11 wherein said axes of vibrationare substantially orthogonal.

13. A gyroscope comprising: support means; first and second inertialelements; first and second suspension means for t-orsionally couplingsaid first and second inertial elements, respectively, to said supportmeans, said first and second suspension means being orthogonal; andmeans for rotating said support means.

14. The gyroscope of claim 13 further comprising means responsive to thevibrations of each of said inertial elements for generating outputsignals representative of rotational movements of said inertialinstrument and means coupled to the last recited means for reducing themagnitude of the components of said output signals gen erated byvibrational forces acting on said support means.

15. A gyroscope comprising: support means; a pair of inertial elements;first and second suspension means for torsionally coupling said inertialelements to said support means, said first and second suspension meansbeing substantially parallel and one of said inertial elements havingits center of mass displaced a preselected distance from its point ofsuspension; means for rotating said inertial elements; and meansresponsive to vibratory motions of said inertial elements for generatingoutput signals representative of rotational and accelerational movementsof said gyroscope.

36. An inertial instrument comprising: a frame; first and secondinertial elements rotatable with respect to said frame about apreselected axis, said first and second inertial elements being capableof vibratory motion about first and second axes of vibration angularlydisposed with respect to said preselected axis and each of said inertialelements having its center of mass displaced a preselected distance fromits axis of vibration, the centers of mass of said inertial elementsbeing displaced in opposite directions from their respective axes ofvibration; and means 12. for rotating said first and second inertialelements about said preselected axis.

17. A gyroscope comprising: support means; a plurality of inertialelements; suspension means for torsionally coupling said inertialelements to said support means, at least one of said suspension meansbeing angularly disposed to the others of said suspension means and atleast one of said inertial elements having its center of mass displaceda preselected distance from its center of suspension; and means forrotating said plurality of inertial elements.

18. A gyroscope comprising: support means; a trio of inertial elements;suspension means for t-orsionally coupling said inertial elements tosaid support means, two of said inertial elements having theirsuspension means parallel to one another and orthogonal to thesuspension means of said third inertial element and one of said trio ofinertial elements having its center of mass displaced a preselecteddista cc from its center of suspension; and means for rotating saidsupport means.

19. in an inertial guidance system the combination comprising: a stableelement; and a plurality of gyro scopes positioned on said stableelement along preselected axes, each of said gyroscopes comprising aplurality of inertial elements and means for rotating said plurality ofinertial elements with respect to said stable element about one of saidpreselected axes, said plurality of inertial elements being capable ofvibratory motion about axes of vibration angularly disposed with respectto the axes of rotation of said plurality of inertial elements.

29. The combination of claim 19 wherein the center of mass of at leastone of the plurality of inertial elements in each of said gyroscopes isdisplaced a preselected distance from its axis of vibration.

21. The combination of claim 19 wherein the center of mass of at leastone of the plurality of inertial ele tents of one of said gyroscopes isdisplaced toward the point of intersection of said preselected axes andthe center of mass of at least one of the inertial elements of anotherof said gyroscopes is displaced away from the point of intersection ofsaid preselected axes.

References Cited UNITED STATES PATENTS 2,716,893 9/1955 Birdsall 7453,077,785 2/1963 Stiles 745 3,147,627 9/1964 Hunn 745.6 3,241,377 3/1966Newton 74-5.6

C. I. HUSAR, Primary Examiner.

FRED C. MATTERN, Examiner.

I. D. PUFFER, Assistant Examiner.

1. AN INERTIAL INSTRUMENT COMPRISING: A FRAME; A PLURALITY OF INERTIALELEMENTS ROTATABLE WITH RESPECT TO SAID FRAME ABOUT A FIRST AXIS, SAIDINERTIAL ELEMENTS BEING CAPABLE OF ROTATIONALLY RESTRAINED VIBRATORYMOTION ABOUT AXES OF VIBRATION ROTATING WITH SAID INERTIAL ELEMENTS ANDANGULARLY DISPOSED WITH RESPECT TO SAID FIRST AXIS; AND MEANS FORROTATING SAID INERTIAL ELEMENTS ABOUT SAID FIRST AXIS.